{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T05:58:56Z","timestamp":1769579936913,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T00:00:00Z","timestamp":1585008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant Nos. 41774189 and 61374207"],"award-info":[{"award-number":["Grant Nos. 41774189 and 61374207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bias stability is one of primary characteristics of precise gyroscopes for inertial navigation. Analysis of various sources of the bias drift in a micromachined electrostatically suspended gyroscope (MESG) indicates that the bias stability is dominated by the temperature-induced drift. The analytical results of temperature drift resulting from the rotor structure and capacitive position sensing electronics are modeled and analyzed to characterize the drift mechanism of the MESG. The experimental results indicate that the bias drift is mainly composed of two components, i.e., rapidly changing temperature drift and slowly changing time drift. Both the short-term and long-term bias drift of the MESG are tested and discussed to achieve online bias compensation. Finally, a neural network based-bias compensation scheme is presented and verified experimentally with improved bias stability of the MESG.<\/jats:p>","DOI":"10.3390\/s20061799","type":"journal-article","created":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T13:04:04Z","timestamp":1585055044000},"page":"1799","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Analysis and Compensation of Bias Drift for a Micromachined Spinning-Rotor Gyroscope with Electrostatic Suspension"],"prefix":"10.3390","volume":"20","author":[{"given":"Shunyue","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8425-6764","authenticated-orcid":false,"given":"Fengtian","family":"Han","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.3390\/s140101394","article-title":"The Development of Micromachined Gyroscope Structure and Circuitry Technology","volume":"14","author":"Xia","year":"2014","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1109\/5.704269","article-title":"Micromachined Inertial Sensors","volume":"86","author":"Yazdi","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/JMEMS.2004.824900","article-title":"A self-acting gas thrust bearing for high-speed microrotors","volume":"13","author":"Wong","year":"2004","journal-title":"J. Microelectromech. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2011.08.003","article-title":"Design and characterization of MEMS micromotor supported on low friction liquid bearing","volume":"177","author":"Chan","year":"2012","journal-title":"Sens. Actuators A Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1049\/mnl.2013.0660","article-title":"Optimised geometry model for liquid-suspended miniature gyroscope","volume":"9","author":"Zhang","year":"2014","journal-title":"Micro Nano Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chen, D., Liu, X., and Zhang, H. (2018). A rotational gyroscope with a water-film bearing based on magnetic self-restoring effect. Sensors, 18.","DOI":"10.3390\/s18020415"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"085027","DOI":"10.1088\/0960-1317\/21\/8\/085027","article-title":"Performance of an active electric bearing for rotary micromotors","volume":"21","author":"Han","year":"2011","journal-title":"J. Micromech. Microeng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Sun, B., Wang, S., and Tan, Y. (2018). Spin Rate Effects in a Micromachined Electrostatically Suspended Gyroscope. Sensors, 18.","DOI":"10.3390\/s18113901"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.sna.2006.03.002","article-title":"The study of an electromagnetic levitating micromotor for application in a rotating gyroscope","volume":"132","author":"Zhang","year":"2006","journal-title":"Sens. Actuators A Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/187\/1\/012001","article-title":"Micro\/nano electro mechanical systems for practical applications","volume":"187","author":"Esashi","year":"2009","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_11","first-page":"53","article-title":"Design and fabrication of a micromachined electrostatically suspended gyroscope","volume":"222","author":"Damrongsak","year":"2008","journal-title":"Pro. Inst. Mech. Eng Part C J. Micromech. Microeng Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kraft, M., and Damrongsak, B. (2010, January 1\u20134). Micromachined gyroscopes based on a rotating mechanically unconstrained proof mass. Proceedings of the SENSORS, 2010 IEEE, Kona, HI, USA.","DOI":"10.1109\/ICSENS.2010.5690984"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7001","DOI":"10.1109\/JSEN.2015.2469715","article-title":"Static behavior of closed-loop micromachined levitated two-axis rate gyroscope","volume":"15","author":"Poletkin","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"105032","DOI":"10.1088\/0960-1317\/22\/10\/105032","article-title":"Micromachined electrostatically suspended gyroscope with a spinning ring-shaped rotor","volume":"22","author":"Han","year":"2012","journal-title":"J. Micromech. Microeng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sun, B., Wang, S., and Tan, Y. (2019, January 23\u201327). High-yield triple-stack bonding fabrication process for micromachined micromotors with contactless rotor. Proceedings of the 2019 20th International Conference on Solid-State Sensors, Actuators and Microsystems & Eurosensors XXXIII (TRANSDUCERS & EUROSENSORS XXXIII), Berlin, Germany.","DOI":"10.1109\/TRANSDUCERS.2019.8808462"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4336","DOI":"10.1109\/TIE.2016.2544252","article-title":"Rotation control and characterization of high-speed variable-capacitance micromotor supported on electrostatic bearing","volume":"63","author":"Sun","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1088\/0957-0233\/18\/5\/030","article-title":"Temperature drift modelling and compensation for a dynamically tuned gyroscope by combining WT and SVM method","volume":"18","author":"Xu","year":"2007","journal-title":"Meas. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zotov, S., Simon, B., and Sharma, G. (2014, January 25\u201326). Utilization of mechanical quadrature in silicon MEMS vibratory gyroscope to increase and expand the long term in-run bias stability. Proceedings of the 2014 International Symposium on Inertial Sensors and Systems (ISISS), Laguna Beach, CA, USA.","DOI":"10.1109\/ISISS.2014.6782536"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1016\/j.ijleo.2012.02.008","article-title":"Study on temperature error processing technique for fiber optic gyroscope","volume":"124","author":"Chen","year":"2013","journal-title":"Optik"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Challoner, A., Howard, H., and Liu, J. (2014, January 5\u20138). Boeing disc resonator gyroscope. Proceedings of the 2014 IEEE\/ION Position, Location and Navigation Symposium\u2014PLANS 2014, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2014.6851410"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1109\/TIM.2009.2016780","article-title":"Integrated model and compensation of thermal errors of silicon microelectromechanical gyroscope","volume":"58","author":"Fang","year":"2009","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","first-page":"262","article-title":"Test results of Honeywell\u2019s first-generation high-performance interferometric fiber optic gyroscope","volume":"1585","author":"Liu","year":"1992","journal-title":"Fiber Opt. Gyros Anniv. Conf. Int. Soc. Opt. Photonics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.sna.2012.12.024","article-title":"Compensation of drifts in high-Q MEMS gyroscopes using temperature self-sensing","volume":"201","author":"Prikhodko","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_24","first-page":"239","article-title":"Noise characteristics of MEMS gyro\u2019s null drift and temperature compensation","volume":"15","author":"Shiau","year":"2012","journal-title":"J. Appl. Sci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Prikhodko, I., Nadig, S., and Gregory, J. (2017, January 27\u201330). Half-a-month stable 0.2 degree-per-hour mode-matched MEMS gyroscope. Proceedings of the 2017 IEEE International Symposium on Inertial Sensors and Systems (INERTIAL), Kauai, HI, USA.","DOI":"10.1109\/ISISS.2017.7935679"},{"key":"ref_26","unstructured":"Fukuda, G., and Hayashi, S. (2020, March 23). Inertial Navigation System with MEMS-ESG and Automated Sun Altitude Measuring System using Web-Camera. Available online: http:\/\/nornav.custompublish.com\/getfile.php\/1067052.753.ucpdyrysed\/P%2014.pdf."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wang, S., Han, F., and Sun, B. (2017). Squeeze-Film Air Damping of a Five-Axis Electrostatic Bearing for Rotary Micromotors. Sensors, 17.","DOI":"10.3390\/s17051119"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1007\/s00542-005-0603-8","article-title":"Reliability of MEMS packaging: Vacuum maintenance and packaging induced stress","volume":"11","author":"Choa","year":"2005","journal-title":"Microsyst. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1109\/JSEN.2007.896560","article-title":"A device-level vacuum-packaging scheme for microbolometers on rigid and flexible substrates","volume":"7","author":"Mahmood","year":"2007","journal-title":"IEEE Sens. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1109\/JMEMS.2006.876798","article-title":"Device-level hermetic packaging of microresonators by RTP aluminum-to-nitride bonding","volume":"15","author":"Chiao","year":"2006","journal-title":"J. Microelectromech. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Zhang, Q., Tan, Z., and Guo, L. (2009, January 19\u201320). Compensation of temperature drift of MEMS gyroscope using BP neural network. Proceedings of the 2009 International Conference on Information Engineering and Computer Science, Wuhan, China.","DOI":"10.1109\/ICIECS.2009.5365140"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/6\/1799\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:11:10Z","timestamp":1760173870000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/6\/1799"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,24]]},"references-count":31,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["s20061799"],"URL":"https:\/\/doi.org\/10.3390\/s20061799","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,24]]}}}